Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-3x+2y &= 2 \\ -6x-2y &= -5\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-6x = 2y-5$ Divide both sides by $-6$ to isolate $x$ $x = {-\dfrac{1}{3}y + \dfrac{5}{6}}$ Substitute this expression for $x$ in the first equation. $-3({-\dfrac{1}{3}y + \dfrac{5}{6}}) + 2y = 2$ $y - \dfrac{5}{2} + 2y = 2$ Simplify by combining terms, then solve for $y$ $3y - \dfrac{5}{2} = 2$ $3y = \dfrac{9}{2}$ $y = \dfrac{3}{2}$ Substitute $\dfrac{3}{2}$ for $y$ in the top equation. $-3x+2( \dfrac{3}{2}) = 2$ $-3x+3 = 2$ $-3x = -1$ $x = \dfrac{1}{3}$ The solution is $\enspace x = \dfrac{1}{3}, \enspace y = \dfrac{3}{2}$.